# Lennard-Jones 6-12 potential

1. Mar 7, 2013

### ProPatto16

1. The problem statement, all variables and given/known data
Deduce the form of the Lennard-Jones potential between two water molecules.

given/known:
molar enthalpy of evaporation of water is 4.1x104J/mol
density is 103kg/m3
Assume water molecule is surrounded by approximately ten nearest-neighbours.
Take Mr = 18

2. Relevant equations

from the sources i have:
V(r)=4ε[-(σ/r)6+(σ/r)12]

3. The attempt at a solution

ε is a measure of how strongly the molecules attract each other.
σ is the distance at which the intermolecular potential is zero.
r is the distance of seperation between both particles.

its a bit unclear what the question means by "deduce the form" but im assuming it means find the value r.

to find r i first find the atomic diameter d= [(Mr(X)x10-3)/(pNA)]1/3

where X is number of molecules
Mr = 18
p given at 103kg/m3

and X im unsure if it is 2 (because the question says two molecules) or if its 11 (because of the molecule plus its 10 "neighbours")

if X is 2 i get a diameter of 1.815x10-10

if X is 11 i get d = 3.20x10-10
making r = 1.60x10-10

now to get the "form" i just sub an r into the potential equation??

however, i dont entirely understand the "ten nearst-neighbours" and what its used for.
i also dont use the molar enthalpy.
molar enthalpy isnt mentioned anywhere in my notes but online it says enthlpy is a measure of energy of the system.

some clarification would be much appreciated
thanks
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 8, 2013

### ProPatto16

kept at it and found

molecular enthalpy of sublimation Hm.s = 1/2(nNAΔE)
where n is the number of "nearest neighbours"
solving for ΔE i got 1.36x10-20 J which seems appropriate.

and ΔE = ε when r is at equilibrium distance.

so subbing that back into the lennard-jones and simplifying i get

5.44x10-20[-(σ/0.72x10-10)6+(σ/0.72x10-10)12]

is that meant to be "the form of the Lennard-Jones 6-12 potential" that the question says deduce?